The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0 X^2  1  1  1  1 X^2+X+2  X X+2  1  1  1  1  X X^2+X+2 X^2  2  1 X^2+X+2  1  0 X^2+2  1  0  1  1  1  1 X^2  X X^2+X+2  X  1 X^2+2  1  1 X+2 X^2+X+2  1  1  1
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1  X X+2  X X^2+X+3 X^2+X+1 X^2+2  1  1 X+3 X^2+X+2 X+1 X^2+X X^2+X  1 X^2  1  0  1 X+1 X^2+2 X^2+X X^2+X+2  1  1  3 X+2  2  1  1  1 X^2 X^2+X+3  1  X X^2+3  1  1 X^2+X+3  1 X^2+1
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X+2 X^2+3 X+1  X  1 X^2+X+1  X  2 X+3  1 X^2  1 X+1  1 X+3 X^2+X+3 X^2+2 X^2+X+1  1  1 X+2 X^2+1 X^2+2  3 X^2+X+1 X^2  3 X^2+3  X  1  2 X+3  1  3 X^2+X+2 X^2+X+1 X^2+X X^2+X X^2+X+1

generates a code of length 53 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+530x^50+740x^51+818x^52+576x^53+490x^54+288x^55+263x^56+112x^57+127x^58+76x^59+68x^60+4x^62+2x^64+1x^66

The gray image is a code over GF(2) with n=424, k=12 and d=200.
This code was found by Heurico 1.16 in 49.1 seconds.